Some cases of bifurcation in elastic-plastic solids in plane strain
Authors:
S. T. Ariaratnam and R. N. Dubey
Journal:
Quart. Appl. Math. 27 (1969), 349-358
DOI:
https://doi.org/10.1090/qam/99819
MathSciNet review:
QAM99819
Full-text PDF Free Access
Abstract |
References |
Additional Information
Abstract: Conditions for initiation of necking, buckling and surface instabilities in an elastic-plastic solid in plane strain are derived. The results constitute a generalization of previous investigations for rigid-plastic and elastic solids.
- Maurice A. Biot, Mechanics of incremental deformations. Theory of elasticity and viscoelasticity of initially stressed solids and fluids, including thermodynamic foundations and applications to finite strain, John Wiley & Sons, Inc., New York-London-Sydney, 1965. MR 0185873
G. R. Cowper and E. T. Onat, The initiation of necking in plane plastic flow, Proc. 4th U. S. Natl. Cong. Appl. Mech., 1023–1029 (1962)
R. Hill, A general theory of uniqueness and stability in elastic-plastic solid, J. Mech. Phys. Solids, 6, 236–249 (1958)
E. H. Lee, Plastic flow in V-notched bar pulled in tension, J. Appl. Mech. 19, 331–336 (1952)
- E. T. Onat and W. Prager, The necking of a tension specimen in plane plastic flow, J. Appl. Phys. 25 (1954), 491–493. MR 62627
- Alexander J. Wang, Plastic flow in a deeply notched bar with semi-circular root, Quart. Appl. Math. 11 (1954), 427–438. MR 58437, DOI https://doi.org/10.1090/S0033-569X-1954-58437-4
- Zbigniew Wesołowski, Stability in some cases of tension in the light of the theory of finite strain, Arch. Mech. Stos. 14 (1962), 875–900 (English, with Russian and Polish summaries). MR 149744
M. A. Biot, Mechanics of incremental deformation, John Wiley and Sons, New York, 1965
G. R. Cowper and E. T. Onat, The initiation of necking in plane plastic flow, Proc. 4th U. S. Natl. Cong. Appl. Mech., 1023–1029 (1962)
R. Hill, A general theory of uniqueness and stability in elastic-plastic solid, J. Mech. Phys. Solids, 6, 236–249 (1958)
E. H. Lee, Plastic flow in V-notched bar pulled in tension, J. Appl. Mech. 19, 331–336 (1952)
E. T. Onat and W. Prager, The necking of a tension specimen in plane plastic flow, J. Appl. Phys., (4) 25, 491–493 (1954)
A. J. Wang, Plastic flow in deeply notched bar with semicircular root, Quart. Appl. Math. 11, 427–438 (1954)
Z. Wesolowski, Stability in some cases of tension in the light of the theory of finite strain, Arch. Mech. Stos. (6) 14, 875–898 (1962)
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Article copyright:
© Copyright 1969
American Mathematical Society
